Learning a hyperelastic constitutive model from 3D experimental data

The accuracy of the rubber constitutive model characterizing experiment data has a crucial influence on the mechanical analysis of rubber structures. In this paper, a new improved hyperelastic constitutive model is proposed, and the model is derived into the stress-strain forms of uniaxial tension, equibiaxial tension and pure shear. Based on the experimental data of filled rubber, the material parameters of each deformation state are obtained by using the newly proposed rubber hyperelastic constitutive model, and the uniaxial tensile (UT), Equibiaxial tension (ET) and Pure shear (PS) specimens are simulated and calculated in the finite element software. the stress state of each finite element specimen is analyzed and the obtained simulation data are compared with the experimental data. It is found that the new model can accurately characterize the hyperelastic mechanical properties of the experimental specimens in different deformation states. At the same time, the reasons for the deviation from the experimental data in the process of plane tensile simulation are analyzed and explained comprehensively. The reliability and accuracy of the classical rubber constitutive relations of polynomial models and eight-chain model are studied. the results show that different hyperelastic models have different ability to describe the hyperelastic behavior in different deformation states. the hyperelastic constitutive model proposed in this paper can be easily embedded into finite element software and has the advantages of accurate results, few material parameters and simple testing.

Several authors have proposed different parameters to include the softening effect in hyperelastic models; however, for a number of materials, softening parameters could be further improved. This article proposes a new softening parameter to include Mullins effect in hyperelastic material models. The methodology employed can be also used in cases with hysteresis or damage in a hyperelastic material, however this methodology modifies the behavior of the material differently from damage theories. Common hyperelastic constitutive models do not include dissipation effects and so the present work intends to fill this gap. Experimental data for silicone in uniaxial tensile test, equibiaxial, and pure shear tests were modeled in order to calibrate the models. The softening parameters essentially changes the constitutive law from the loading to the unloading path. Therefore, it is still necessary to use a hyperelastic model, and here Ogden and Hoss-Marczak material models were used. The obtained results show good agreement with experimental data even when simulating with a compressible finite element code and it can model isotropic Mullins effect.

Hyperelastic constitutive modeling of hydrogels based on primary deformation modes and validation under 3D stress states

High quality computational model of soft tissues is a function of accurate and reliable mechanical properties. Hyperelastic constitutive models are normally utilised in developing reliable computational models. Therefore, section of proper and reliable constitutive models for soft tissue is critical. This work presents the biomechanical properties of oesophagus subjected to biaxial mechanical tensile test. Additionally, six hyperelastic constitutive models commonly used for modelling behaviour of soft tissues were selected. The experimental data were then fitted on Fung, Choi-Vito, Holzapfel (2000), Holzapfel (2005), Polynomial (Anisotropic) and Four-Fiber Family hyperelastic constitutive models. The sheep oesophagus subjected to equi-biaxial tension has exhibited different stress magnitude in both longitudinal and circumferential directions. There is significant difference between circumferential and longitudinal stresses (p = 0.0034). The average circumferential and longitudinal stresses are recorded to be 82.87 ± 30.36 kPa and 41.42 ± 32.02 kPa, respectively (p = 0.0034). Between six hyperelastic constitutive models, it was observed that Four-Fiber model has produced better fit when compared to others. After fitting biaxial mechanical properties of oesophagus, it was found that the Four-fiber family hyperelastic constitutive model would best fit.

Integrating theoretical and experimental approaches for annulus fibrosus (AF) functional tissue engineering. Apply a hyperelastic constitutive model to characterize the evolution of engineered AF via scalar model parameters. Validate the model and predict the response of engineered constructs to physiologic loading scenarios. There is need for a tissue engineered replacement for degenerate AF. When evaluating engineered replacements for load-bearing tissues, it is necessary to evaluate mechanical function with respect to the native tissue, including nonlinearity and anisotropy. Aligned nanofibrous poly-epsilon-caprolactone scaffolds with prescribed fiber angles were seeded with bovine AF cells and analyzed over 8 weeks, using experimental (mechanical testing, biochemistry, histology) and theoretical methods (a hyperelastic fiber-reinforced constitutive model). The linear region modulus for phi = 0 degrees constructs increased by approximately 25 MPa, and for phi = 90 degrees by approximately 2 MPa from 1 day to 8 weeks in culture. Infiltration and proliferation of AF cells into the scaffold and abundant deposition of s-GAG and aligned collagen was observed. The constitutive model had excellent fits to experimental data to yield matrix and fiber parameters that increased with time in culture. Correlations were observed between biochemical measures and model parameters. The model was successfully validated and used to simulate time-varying responses of engineered AF under shear and biaxial loading. AF cells seeded on nanofibrous scaffolds elaborated an organized, anisotropic AF-like extracellular matrix, resulting in improved mechanical properties. A hyperelastic fiber-reinforced constitutive model characterized the functional evolution of engineered AF constructs, and was used to simulate physiologically relevant loading configurations. Model predictions demonstrated that fibers resist shear even when the shearing direction does not coincide with the fiber direction. Further, the model suggested that the native AF fiber architecture is uniquely designed to support shear stresses encountered under multiple loading configurations.

We characterize the material properties of a woven, multi-layered, hyperelastic composite that is useful as an envelope material for high-altitude stratospheric airships and in the design of other large structures. The composite was fabricated by sandwiching a polyaramid Nomex® core, with good tensile strength, between polyimide Kapton® films with high dielectric constant, and cured with epoxy using a vacuum bagging technique. Uniaxial mechanical tests were used to stretch the individual materials and the composite to failure in the longitudinal and transverse directions respectively. The experimental data for Kapton® were fit to a five-parameter Yeoh form of nonlinear, hyperelastic and isotropic constitutive model. Image analysis of the Nomex® sheets, obtained using scanning electron microscopy, demonstrate two families of symmetrically oriented fibers at 69.3°± 7.4° and 129°± 5.3°. Stress-strain results for Nomex® were fit to a nonlinear and orthotropic Holzapfel-Gasser-Ogden (HGO) hyperelastic model with two fiber families. We used a linear decomposition of the strain energy function for the composite, based on the individual strain energy functions for Kapton® and Nomex®, obtained using experimental results. A rule of mixtures approach, using volume fractions of individual constituents present in the composite during specimen fabrication, was used to formulate the strain energy function for the composite. Model results for the composite were in good agreement with experimental stress-strain data. Constitutive properties for woven composite materials, combining nonlinear elastic properties within a composite materials framework, are required in the design of laminated pretensioned structures for civil engineering and in aerospace applications.

Hyper-elastic modeling and mechanical behavior investigation of porous poly-D-L-lactide/nano-hydroxyapatite scaffold material

In this paper, we identified the material constitutive parameters of the human skull from reported tensile test results. Initially, we applied both linear-elastic and Mooney–Rivlin nonlinear hyperelastic constitutive models to the available tensile test data at different strain rates of 0.005, 0.10, 10, and 150 1/sec. It was shown that the suggested hyperelastic model fitted the test results with higher accuracy in comparison with the linear-elastic model. In the next step, the experimental modal analysis was carried out through roving hammer-impact tests on a dried human skull. The first four natural frequencies of the skull were measured to be 496, 543, 1250, and 1287 Hz, and these values were verified by the modal assurance criterion. Then, a 3D finite element (FE) model of that human skull was created by a 3D scanner and discretized to carry out a computational modal analysis. The performance of the determined material properties for the human skull from both linear and hyperelastic material models was evaluated using FE modal analysis. The calculated modal frequencies were then compared to the experimentally measured frequencies. It was shown that the material parameters from both the linear and hyperelastic constitutive models obtained at a strain rate of 0.10 1/sec, provided the best performance in computational modal analysis with minimum deviations relative to the experimental results. These results confer a better understanding of the human skull behavior among different strain rates, which could increase the accuracy of nonlinearity dynamic simulations on the skull.

The unstable behavior of the isotropic, compressible Mooney-Rivlin hyperelastic model is investigated and described. The constitutive equation is parameterized with the help of the ground-state Poisson’s ratio and the dimensionless ratio of the material parameters [Formula: see text] and [Formula: see text]. Transverse stretch solutions are obtained for standard homogeneous loading modes, and the stress solutions are computed numerically for the physically permitted range of the ground-state Poisson’s ratio. We introduce a numerical technique to isolate subdomains with non-unique transverse stretch responses. Our analysis revealed some limitations of the model and allowed us to make critical observations about the strengths and weaknesses of the model. The analyses we present are essential to understand the characteristics of this widely used hyperelastic model. The novel results have important implications for the application of the isotropic, compressible Mooney-Rivlin hyperelastic material model.

Recent advances in the numerical modeling of constitutive relations

BackgroundLinear elastic, hyperelastic, and multiphasic material constitutive models are frequently used for spinal intervertebral disc simulations. While the characteristics of each model are known, their effect on spine mechanical response requires a careful investigation. The use of advanced material models may not be applicable when material constants are not available, model convergence is unlikely, and computational time is a concern. On the other hand, poor estimations of tissue’s mechanical response are likely if the spine model is oversimplified. In this study, discrepancies in load response introduced by material models will be investigated.MethodsThree fiber-reinforced C2-C3 disc models were developed with linear elastic, hyperelastic, and biphasic behaviors. Three different loading modes were investigated: compression, flexion and extension in quasi-static and dynamic conditions. The deformed disc height, disc fluid pressure, range of motion, and stresses were compared.ResultsResults indicated that the intervertebral disc material model has a strong effect on load-sharing and disc height change when compression and flexion were applied. The predicted mechanical response of three models under extension had less discrepancy than its counterparts under flexion and compression. The fluid-solid interaction showed more relevance in dynamic than quasi-static loading conditions. The fiber-reinforced linear elastic and hyperelastic material models underestimated the load-sharing of the intervertebral disc annular collagen fibers.ConclusionThis study confirmed the central role of the disc fluid pressure in spinal load-sharing and highlighted loading conditions where linear elastic and hyperelastic models predicted energy distribution different than that of the biphasic model.

Calibration of hyperelastic and hyperfoam constitutive models for an indentation event of rigid polyurethane foam

Accurate estimation of the wall stress distribution in an abdominal aortic aneurysm (AAA) may prove clinically useful by predicting when a particular aneurysm will rupture. Appropriate constitutive models for both the wall and the intraluminal thrombus (ILT) found in most AAA are necessary for this task. The purpose of this work was to determine the mechanical properties of ILT within AAA and to derive a more suitable constitutive model for this material. Uniaxial tensile testing was carried out on 50 specimens, including 14 longitudinally oriented and 14 circumferentially oriented specimens from the luminal region of the ILT, and 11 longitudinally oriented and 11 circumferentially oriented specimens from the medial region. A two-parameter, large-strain, hyperelastic constitutive model was developed and used to fit the uniaxial tensile testing data for determination of the material parameters. Maximum stiffness and strength were also determined from the data for each specimen. Scanning electron microscopy (SEM) was conducted to study the regional microstructural difference. Our results indicate that the microstructure of ILT differs between the luminal, medial, and abluminal regions, with the luminal region stronger and stiffer than the medial region. In all cases, the constitutive model fit the experimental data very well (R2>0.98). No significant difference was found for either of the two material parameters between longitudinal and circumferential directions, but a significant difference in material parameters, stiffness, and strength between the laminal and medial regions was determined (p<0.01). Therefore, our results suggest that ILT is an inhomogeneous and possibly isotropic material. The two-parameter, hyperelastic, isotropic, incompressible material model derived here for ILT can be easily incorporated into finite element models for simulation of wall stress distribution in AAA.

Design of experiments on the effects of linear and hyperelastic constitutive models and geometric parameters on polymer electrolyte fuel cell mechanical and electrical behaviour

This paper presents a numerical technique to determine the full pre-buckling and post-buckling equilibrium path for elastic funicular arches. The formulation includes the effects of shear deformations and geometric nonlinearity due to large deformations. The Timoshenko beam hypothesis is adopted for incorporating shear. Finite strains are considered without approximation. The finite strains are defined in terms of the normal and shear component of the longitudinal stretch. The constitutive relations for the internal actions are based on a hyperelastic constitutive model. Using the differential equilibrium equations and the constitutive laws, the nonlinear buckling behavior of some typical funicular arches are investigated using the trapezoid method with Richardson extrapolation enhancement. The results are validated by using the finite element package ANSYS and solutions available in the literature. Examples include parabolic arches under a uniformly distributed gravity load, a catenary under a distributed load along the arch and a catenary arch under an overburden load. Parametric studies are performed to identify the factors that influence the nonlinear buckling of funicular arches. The axial to shear rigidity ratio is shown to have a significant effect on the buckling load and the buckling mode shape.